If you could choose to live in one period of history....

Being at heart a coward, I would have liked to have been born American in 1905; too young for WWI, too old for WWII. I would like to have been a journalist or working for the government in some research or intelligence gathering capacity. I find the time period 1900-1945 to be the most interesting period of any history I've read. The prelude to the Great War, WWI, the Roaring '20s, the growth of fascism and militarism around the globe, the Great Depression, then WWII. But it was also the era of remarkable technological growth and improvements in medicine, transportation, communication... IMO just a fascinating period of history.

Interesting.
Are you sure being born in 1905 would have ensured you would have avoided fighting in WWII?
Definitely an interesting period. Depends if you want interesting or pleasant. The Chinese phrase "may you live in interesting times" is after all, a curse!
Germany in 1945 was after all "interesting" as was the US in 1863, Russia in 1918 and France in 1792!
Not thought of my own answer yet...

Personally, I'd rather take vacations in different periods rather than live in them, using a time machine that means I cannot effect the course of history (so nothing that I do actually happened when I return to the present day).

I like to take vacations in:
Late-1940s New York City
1957 in Melbourne, Australia
1975, in a nice suburb somewhere in the US (really so I can watch all the fabulous daytime game shows of that year)
1957 in London, England
1912, in New York City
Also, if someone can invent a time machine that allows that, should I die while visiting the past, I simply wake up in the modern day unharmed, I would like be a celt, a saxon, and a medieval soldier, and perhaps also a musketeer.

Have you played Atari today?

Cool. Why the London 1957 one?

Partly to watch the TV (particularly given that nearly all the programs are lost) and listen to the radio (ditto). Would also be interesting to see the final days of music hall, and look around camera shops and such.

EDIT: I'm surprised somebody doesn't create a museum that is an exact recreation of a mid-century set of shops.

Have you played Atari today?

I've got a box full of mp3s of old time radio programs, which were in their dying days when I was a boy but I remember hearing some of them. Many of the shows had gone on to tv by then, or they would very soon.

definitely Tudor times here in England

If I could be wealthy, it would definitely be Ancient Rome for me during the Julio-Claudian dynasty.